1. Field of the Invention
The present invention relates to a method and a tool for machining a three dimensional surface, and in particular, to a method of three dimensional surface machining such as by cutting or grinding and electrical shaping such as by discharge or electrolysis and to a tool for three dimensional surface work to be used in the method.
2. Description of the Prior Art
Conventionally, when machining a three dimensional surface, a tool like a ball end mill has generally been used because of the ease in selection of the tool and in the calculation for the proper positioning of the tool, where the tool (FIG. 11) constitutes a portion of a circle in projected shape (referred to as a projection of a cutting edge below) obtained by graphically projecting the locus of points comprising the outer-most cutting portion of the tool being used for the machining of a workpiece, onto a plane parallel to the longitudinal axis of the tool, said cutting portion of the tool being a cutting edge directly contributing to the machining, for example, a portion (referred to as a cutting edge below) corresponding to a machining portion of a discharge electrode. In FIG. 11, reference numeral 1 indicates the center axis of the rotation of the tool. In this case, to select a tool, the radius R of the tip of the tool need only be smaller than the minimum radius of curvature of the recessed portion of the three dimensional surface (referred to as a machining surface below) of a workpiece to be machined and the tool position is determined by use of a vector having a magnitude of the radius R of the tool along the direction of the normal at the machining position in the machining surface, regardless of the position of the machining point in the circle of the cutting edge; that is, the tool position is set so that the cutting edge of the tool is brought into contact with the workpiece, which is relatively easy if the necessary information about the machining surface is obtained.
However, the curvature of the work surface of the workpiece generally varies from point to point, and hence, when the projection of the cutting edge is a circle, if the machining surface has a recessed portion with a small radius of curvature, the recessed portion must necessarily be the reference for selecting a tool so as to prevent undercut. This leads to the restriction that a tool with a small radius must be used. As such, other portions having considerably greater radii must be machined with the tool having a smaller radius, thereby causing disadvantages with respect to work efficiency and/or desired surface smoothness. That is, as the radius of the tool is decreased work efficiency is lowered if the predetermined smoothness of the finished surface is to be maintained. The finished surface becomes relatively rough if machining efficiency is not sacrificed, due to portions of the work (machining) surface remaining between incremental machined areas of the surface.